daij, koj, gg5, prog, wisdom

I don't think sense 2 is that dated. Or, at least, it's not as dated as sense 3. It's in all the JEs (GG5 leads with it) and none of the other kokugos describe it as 古風, including the most recent edition of meikyo.
I think the archaic sense can be dropped.
Added kanji form.

@@ -6,0 +7,3 @@
+</k_ele>
+<k_ele>
+<keb>真</keb>
@@ -18,0 +22 @@
+<gloss>fact</gloss>
@@ -22 +25,0 @@
-<misc>&dated;</misc>
@@ -25,2 +28,2 @@
-<gloss>integrity</gloss>
-<gloss>fidelity</gloss>
+<gloss>faithfulness</gloss>
+<gloss>good faith</gloss>
@@ -38,6 +40,0 @@
-</sense>
-<sense>
-<pos>&int;</pos>
-<misc>&arch;</misc>
-<s_inf>used when recalling forgotten information, suddenly changing the subject, etc.</s_inf>
-<gloss>that's right</gloss>

Dropping the [adv] tags from the first two senses, which are only tagged as nouns in the kokugos. Sankoku describes sense [2] as 古風.

Adding a new adverbial sense from the kokugos. Shinmeikai defines it as "「まことに」の省略表現。" and Sankoku says it's also 古風. I'm copying our glosses from entries 2820720 (じつに) and 1381160 (まことに).

Changing the final sense from [adv,n] to [int]. It's not in the smaller kokugos and daijirin has it tagged as '感'

@@ -16 +15,0 @@
-<pos>&adv;</pos>
@@ -22 +20,0 @@
-<pos>&adv;</pos>
@@ -23,0 +22 @@
+<misc>&dated;</misc>
@@ -31 +30,11 @@
-<pos>&n;</pos>
+<misc>&dated;</misc>
+<gloss>indeed</gloss>
+<gloss>really</gloss>
+<gloss>absolutely</gloss>
+<gloss>truly</gloss>
+<gloss>actually</gloss>
+<gloss>very</gloss>
+<gloss>quite</gloss>
+</sense>
+<sense>
+<pos>&int;</pos>

@@ -33 +33,2 @@
-<gloss>that's right (used when recalling forgotten information, suddenly changing the subject, etc.)</gloss>
+<s_inf>used when recalling forgotten information, suddenly changing the subject, etc.</s_inf>
+<gloss>that's right</gloss>